Publication Date
Spring 4-16-2025
Presentation Length
20 minutes
College
College of Sciences & Mathematics
Department
Math and Computer Science, Department of
Student Level
Undergraduate
SPARK Category
Scholarship
Faculty Advisor
Adam Cartisano
WELL Core Type
Intellectual Wellness
Metadata/Fulltext
Fulltext
SPARK Session
Geometry Topics
Presentation Type
Talk/Oral
Summary
In the study of Pythagorean triples (PT's) of integers $(a,b,c)$ satisfying $a^2+b^2=c^2$, it is natural to wonder: do we learn anything new by considering the triples of the form $(\pm a, \pm b, c)$? What about the triple $(b,a,c)$? The analysis of primitive PT's (PPT's), viewed as rational points on the unit circle, behaves predictably depending on one's answer to either question. In the former, one can quadrisect the unit circle and perform an analysis on each quadrant. In this talk, we focus on proving a bijection between two types of PT's, establishing a double cover of the set of PPT's by the set of rational numbers, under the assumption that $(a,b,c)\sim(b,a,c)$.
Recommended Citation
Admiraal, Cara, "A Theorem on Parity That's so Odd, You Can't Even" (2025). SPARK Symposium Presentations. 431.
https://repository.belmont.edu/spark_presentations/431
